In order to improve riding comfort or reduce cabin noise, a structure has been proposed that provides vibration damping in a wheel bearing apparatus for mounting a tire wheel or brake disc. A structure, that includes a cylindrical vibration damping member, is arranged between a wheel hub, for mounting a wheel, and an inner ring. In one example shown in FIG. 9, an elastic member 55 is interposed between inner rings 51, 52 of a double row rolling bearing 50 and an outer joint member 54 of a constant velocity universal joint 53. It suppresses transmission of vibration to the double row rolling bearing 50 while damping the vibration of the constant velocity universal joint 53 by the elastic member 55. This improves the bearing life while suppressing the fretting wear of the bearing from the vibration. Such vibration damping members, i.e., elastic member 55, comprises polymer materials such as thermoplastic, elastomer etc. or a vibration damping steel plate with a polymer material sandwiched by normal steel plate (see e.g., JP2001-246903A).
However, a problem exists in that the vibration damping material of the polymer material, such as rubber of the prior art, even though it exhibits a high vibration absorbing effect relative to a high frequency range above several thousand Hz, it cannot exhibit a sufficient damping effect relative to resonation noise (road noise) of 200˜300 Hz caused by vibration of a rubber tire running on an uneven road when secured to the wheel hub of the vehicle. Another problem of the prior art is that the vibration damping member lacks durability when high eccentric loads are repeatedly or long term applied onto the wheel hub. Thus, this tends to cause permanent strains by the eccentric loads.